00:01
Hello, the question deals with mathematical modeling.
00:04
Pt is equal to p .0 e -raise to the power kt denotes the exponential growth model.
00:16
Now, according to the question in the year 1940, that corresponds to time is equal to zero, the population is 131 .7 million which is the initial population.
00:40
So the expression that is the growth model is pt is equal to 131 .7 e -raise to the power kt.
00:52
Now, in the year 2000, which corresponds to time, t is equal to 60, the population pt is equals to 281 .4 million.
01:11
So using this information, we compute the value of k.
01:17
281 .4 is equals to 131 .4.
01:22
7, e raised to the power 60k.
01:26
Solving for the value of k, we obtained e raised to the power 60k is equals to 2 .14.
01:38
Take in natural log on both sides and simplifying we obtained k is equals to 0 .7608 divided by 60...